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Let X and Y be Bernoulli random variables. Let Z = X+ Y.a.

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 4E Chapter 4.1

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 4E

Let X and Y be Bernoulli random variables. Let Z = X+ Y.

a. Show that if X and Y cannot both be equal to 1, then Z is a Bernoulli random variable.

b. Show that if X and Y cannot both be equal to 1, then pz=px+py

c. Show that if X and Y can both be equal to 1, then Z is not a Bernoulli random variable.

Step-by-Step Solution:

Answer:

Step 1 of 3:

(a)

In this question, we are asked to prove that if   and  cannot both be equal to 1, then is a Bernoulli random variable.

Let  and  be Bernoulli random variables. Let  = .

Case 1:

If and ,

Case 2:

If and ,

So in both the cases .

The random variable  is said to have the Bernoulli distribution when random event results in the success, then . Otherwise .

So from the definition we can say that  is also a Bernoulli random variable.

Since value of .

Hence proved.

Step 2 of 3:

(b)

In this question, we are asked to prove that if   and  cannot both be equal to 1, then

From the addition rule of probability, we have

 =   ……….(1)

Since  and  cannot both be equal to 1.

Hence ,

we can rewrite equation (1) as,

 =

,  and  

Substitute above values, we have

Hence proved.

Step 3 of 3

Chapter 4.1, Problem 4E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

The full step-by-step solution to problem: 4E from chapter: 4.1 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This full solution covers the following key subjects: Bernoulli, both, show, random, equal. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. Since the solution to 4E from 4.1 chapter was answered, more than 1004 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “Let X and Y be Bernoulli random variables. Let Z = X+ Y.a. Show that if X and Y cannot both be equal to 1, then Z is a Bernoulli random variable.________________b. Show that if X and Y cannot both be equal to 1, then pz=px+py________________c. Show that if X and Y can both be equal to 1, then Z is not a Bernoulli random variable.” is broken down into a number of easy to follow steps, and 66 words.

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